A battle between the two best defences in La Liga was unsurprisingly settled by a single goal when the Italian turned home Cedric Bakambu's cross eight minutes from time.
Victory hauls Villarreal to within five points of fourth-placed Sevilla, who have a game in hand, and eight of Atletico in third.
In-form Atletico get job done against Malaga
Atletico enjoyed the vast majority of the play and chances, but were undone by a brilliant performance by Andres Fernandez in the Villarreal goal.
"Many times we have won this way and today it was our turn to lose," said Atletico boss Diego Simeone. "We played well and went looking for the goal the whole game but the ball didn't want to go in."
Fernandez made a stunning double save early on as Angel Correa wriggled free inside the area to fire goalwards before Saul Niguez's powerful header was turned to safety.
Real defender Pepe suffers broken ribs
The Villarreal stopper also denied the on-form Antoine Griezmann and Nico Gaitan before the break.
Gaitan then had Atletico's best chance of the game early in the second-half. However, he failed to reward boss Diego Simeone for a rare start as again he was denied by Fernandez's outstretched hand.
At the bottom of the table, Tony Adams remains without a point in three matches in charge at Granada after Sandro Ramirez's double earned Andalusian rivals Malaga a 2-0 win at Nuevo Los Carmenes.
Defeat means Granada could now be relegated as early as Saturday should they fail to win at Real Sociedad and Leganes beat Las Palmas on Wednesday.
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